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Robust Regression using Probability Plots for Estimating the Weibull Shape Parameter
Author(s) -
Zhang L.F.,
Xie M.,
Tang L.C.
Publication year - 2006
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.778
Subject(s) - weibull distribution , censoring (clinical trials) , outlier , statistics , robust regression , ordinary least squares , mathematics , linear regression , regression analysis , shape parameter , estimation theory , regression
Abstract The Weibull shape parameter is important in reliability estimation as it characterizes the ageing property of the system. Hence, this parameter has to be estimated accurately. This paper presents a study of the efficiency of using robust regression methods over the ordinary least‐squares regression method based on a Weibull probability plot. The emphasis is on the estimation of the shape parameter of the two‐parameter Weibull distribution. Both the case of small data sets with outliers and the case of data sets with multiple‐censoring are considered. Maximum‐likelihood estimation is also compared with linear regression methods. Simulation results show that robust regression is an effective method in reducing bias and it performs well in most cases. Copyright © 2006 John Wiley & Sons, Ltd.